Aula 1 mecanica dos fluidos

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1-Considerações Básicas
Sandro R. Lautenschlager
Mecânica dos Fluidos
Aula 1
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Mecânica dos Fluidos
Definição
Estudo dos líquidos e gases no qual não há movimento (estáticos) e naqueles no qual há movimentos (dinâmica)
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History
Faces of Fluid Mechanics
Archimedes
(C. 287-212 BC)
Newton
(1642-1727)
Leibniz
(1646-1716)
Euler
(1707-1783)
Navier
(1785-1836)
Stokes
(1819-1903)
Reynolds
(1842-1912)
Prandtl
(1875-1953)
Bernoulli
(1667-1748)
Taylor
(1886-1975)
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Weather & Climate
Tornadoes
Hurricanes
Global Climate
Thunderstorm
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Vehicles
Aircraft
Submarines
High-speed rail
Surface ships
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Environment
Air pollution
River hydraulics
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Physiology and Medicine
Blood pump
Ventricular assist device
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Sports & Recreation
Water sports
Auto racing
Offshore racing
Cycling
Surfing
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Aplicação em engenharia
Computer Simulations Save US $150,000 in Commuter Jet Design by Reducing Wind Tunnel Testing 
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Aplicação em engenharia
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Aplicação em engenharia
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Aplicação em engenharia
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Propriedades dos Fluidos
Peso específico
Onde:
 g-gravidade local (9,8 m/s2);
r-massa especifica (kg/m3);
g-peso específico (kg/m2s2) ou N/m3
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Propriedades dos Fluidos
Densidade
Temperatura de referência 40C
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Variação de com a temperatura 
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Massa Específica 
Gráf2
		998.9111111111
		999.0611111111
		999.2
		999.3277777778
		999.4444444444
		999.55
		999.6444444444
		999.7277777778
		999.8
		999.8611111111
		999.9111111111
		999.95
		999.9777777778
		999.9944444444
		1000
		999.9944444444
		999.9777777778
		999.95
		999.9111111111
		999.8611111111
		999.8
		999.7277777778
		999.6444444444
		999.55
		999.4444444444
		999.3277777778
		999.2
		999.0611111111
		998.9111111111
		998.75
		998.5777777778
		998.3944444444
		998.2
		997.9944444444
		997.7777777778
		997.55
		997.3111111111
		997.0611111111
		996.8
		996.5277777778
		996.2444444444
		995.95
		995.6444444444
		995.3277777778
		995
		994.6611111111
		994.3111111111
		993.95
		993.5777777778
		993.1944444444
		992.8
Massa Especifica (H2O)
Temperatura (0C)
Massa especifica (kg/m3)
Plan1
		Temperatura (0C)		Massa Especifica (H2O)		Peso Especifivo (H2O)
		-10		998.9111		9789.1111
		-9		999.0611		9790.6111
		-8		999.2000		9792.0000
		-7		999.3278		9793.2778
		-6		999.4444		9794.4444
		-5		999.5500		9795.5000
		-4		999.6444		9796.4444
		-3		999.7278		9797.2778
		-2		999.8000		9798.0000
		-1		999.8611		9798.6111
		0		999.9111		9799.1111
		1		999.9500		9799.5000
		2		999.9778		9799.7778
		3		999.9944		9799.9444
		4		1000.0000		9800.0000
		5		999.9944		9799.9444
		6		999.9778		9799.7778
		7		999.9500		9799.5000
		8		999.9111		9799.1111
		9		999.8611		9798.6111
		10		999.8000		9798.0000
		11		999.7278		9797.2778
		12		999.6444		9796.4444
		13		999.5500		9795.5000
		14		999.4444		9794.4444
		15		999.3278		9793.2778
		16		999.2000		9792.0000
		17		999.0611		9790.6111
		18		998.9111		9789.1111
		19		998.7500		9787.5000
		20		998.5778		9785.7778
		21		998.3944		9783.9444
		22		998.2000		9782.0000
		23		997.9944		9779.9444
		24		997.7778		9777.7778
		25		997.5500		9775.5000
		26		997.3111		9773.1111
		27		997.0611		9770.6111
		28		996.8000		9768.0000
		29		996.5278		9765.2778
		30		996.2444		9762.4444
		31		995.9500		9759.5000
		32		995.6444		9756.4444
		33		995.3278		9753.2778
		34		995.0000		9750.0000
		35		994.6611		9746.6111
		36		994.3111		9743.1111
		37		993.9500		9739.5000
		38		993.5778		9735.7778
		39		993.1944		9731.9444
		40		992.8000		9728.0000
Plan1
		
Massa Especifica (H2O)
Temperatura (0C)
Massa especifica (kg/m3)
Plan2
		
Massa Especifica (H2O)
Temperatura (0C)
Massa especifica (kg/m3)
Plan3
		
		
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Peso Específico
Gráf3
		9789.1111111111
		9790.6111111111
		9792
		9793.2777777778
		9794.4444444444
		9795.5
		9796.4444444444
		9797.2777777778
		9798
		9798.6111111111
		9799.1111111111
		9799.5
		9799.7777777778
		9799.9444444444
		9800
		9799.9444444444
		9799.7777777778
		9799.5
		9799.1111111111
		9798.6111111111
		9798
		9797.2777777778
		9796.4444444444
		9795.5
		9794.4444444444
		9793.2777777778
		9792
		9790.6111111111
		9789.1111111111
		9787.5
		9785.7777777778
		9783.9444444444
		9782
		9779.9444444444
		9777.7777777778
		9775.5
		9773.1111111111
		9770.6111111111
		9768
		9765.2777777778
		9762.4444444444
		9759.5
		9756.4444444444
		9753.2777777778
		9750
		9746.6111111111
		9743.1111111111
		9739.5
		9735.7777777778
		9731.9444444444
		9728
Peso Especifico (H2O)
Temperatura (0C)
Massa especifica (kg/m3)
Plan1
		Temperatura (0C)		Massa Especifica (H2O)		Peso Especifico (H2O)
		-10		998.9111		9789.1111
		-9		999.0611		9790.6111
		-8		999.2000		9792.0000
		-7		999.3278		9793.2778
		-6		999.4444		9794.4444
		-5		999.5500		9795.5000
		-4		999.6444		9796.4444
		-3		999.7278		9797.2778
		-2		999.8000		9798.0000
		-1		999.8611		9798.6111
		0		999.9111		9799.1111
		1		999.9500		9799.5000
		2		999.9778		9799.7778
		3		999.9944		9799.9444
		4		1000.0000		9800.0000
		5		999.9944		9799.9444
		6		999.9778		9799.7778
		7		999.9500		9799.5000
		8		999.9111		9799.1111
		9		999.8611		9798.6111
		10		999.8000		9798.0000
		11		999.7278		9797.2778
		12		999.6444		9796.4444
		13		999.5500		9795.5000
		14		999.4444		9794.4444
		15		999.3278		9793.2778
		16		999.2000		9792.0000
		17		999.0611		9790.6111
		18		998.9111		9789.1111
		19		998.7500		9787.5000
		20		998.5778		9785.7778
		21		998.3944		9783.9444
		22		998.2000		9782.0000
		23		997.9944		9779.9444
		24		997.7778		9777.7778
		25		997.5500		9775.5000
		26		997.3111		9773.1111
		27		997.0611		9770.6111
		28		996.8000		9768.0000
		29		996.5278		9765.2778
		30		996.2444		9762.4444
		31		995.9500		9759.5000
		32		995.6444		9756.4444
		33		995.3278		9753.2778
		34		995.0000		9750.0000
		35		994.6611		9746.6111
		36		994.3111		9743.1111
		37		993.9500		9739.5000
		38		993.5778		9735.7778
		39		993.1944		9731.9444
		40		992.8000		9728.0000
Plan1
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Massa Especifica (H2O)
Temperatura (0C)
Massa especifica (kg/m3)
Plan2
		0
		0
		0
		0
		0
		0
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		0
Peso Especifico (H2O)
Temperatura (0C)
Massa especifica (kg/m3)
Plan3
		
		
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Nas condições Normais
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Some Simple Flows
Flow between a fixed and a moving plate
	Fluid in contact with the plate has the same velocity as the plate
	u = x-direction component of velocity
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Some Simple Flows
Flow through a long, straight pipe
	Fluid in contact with the pipe wall has the same velocity as
the wall
	u = x-direction component of velocity
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Fluid Deformation
Flow between a fixed and a moving plate
Force causes plate to move with velocity V and the fluid deforms continuously.
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Fluid Deformation
Shear stress on the plate is proportional 
to deformation rate of the fluid
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Shear in Different Fluids
Shear-stress relations for different types of fluids
Newtonian fluids: linear relationship
Slope of line (coefficient of proportionality) is “viscosity”
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Viscosity
Newton’s Law of Viscosity
Viscosity
Units
Water (@ 20oC)
 m = 1x10-3 N-s/m2
Air (@ 20oC)
 m = 1.8x10-5 N-s/m2
Kinematic viscosity
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Flow between 2 plates
	
Thus, slope of velocity profile is constant and velocity profile is a st. line
Force is same on top and bottom
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Flow between 2 plates
	
u=V
Moving plate
Fixed plate
y
x
V
u=0
B
Shear stress anywhere between plates
t 
t 
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Flow between 2 plates
2 different coordinate systems
B
V
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Example: Journal Bearing
Given
Rotation rate, w = 1500 rpm
d = 6 cm
l = 40 cm
D = 6.02 cm
SGoil = 0.88
 noil = 0.003 m2/s
Find: Torque and Power required to turn the bearing at the indicated speed.
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Example: cont.
Assume: Linear velocity profile in oil film
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Compressibilidade
Módulo de elasticidade volumétrica
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Módulo de elasticidade para água
B=2100MPa ou 21000x atm
Mudança 1% 
21Mpa (210atm) 
Líquidos podem ser considerados 
incompressíveis
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Cálculo velocidade do som
Exemplo para água c = 1450m/s (condições normais )
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Data da Provas
P1 17/08/11 Cap. 1 e 2;
P2 05/10/11 Cap. 3 e 4;
P3 21/11/11 Cap 4 e 6.
Exame 5/12/11
Avaliação final Cap. 1, 2, 3, 4 e 6
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